Space of modular forms of level 18, weight 4, and Character 18.c

• Label: 18.4.c
• Level: $18$
• Weight: $4$
• Character orbit: 18.c
• Rep. character: $\chi_{18}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(18, [\chi])\).

	Total	New	Old
Modular forms	22	6	16
Cusp forms	14	6	8
Eisenstein series	8	0	8

Trace form

6 * q + 2 * q^2 + 3 * q^3 - 12 * q^4 + 18 * q^5 - 18 * q^6 + 12 * q^7 - 16 * q^8 - 105 * q^9 + 39 * q^11 + 24 * q^12 - 24 * q^13 + 100 * q^14 + 90 * q^15 - 48 * q^16 - 78 * q^17 + 156 * q^18 + 210 * q^19 + 72 * q^20 - 36 * q^21 - 18 * q^22 - 264 * q^23 - 24 * q^24 - 219 * q^25 - 392 * q^26 - 96 * q^28 - 348 * q^29 - 288 * q^30 - 6 * q^31 + 32 * q^32 + 765 * q^33 + 90 * q^34 + 1332 * q^35 + 516 * q^36 + 192 * q^37 + 322 * q^38 - 582 * q^39 - 207 * q^41 - 816 * q^42 + 129 * q^43 - 312 * q^44 - 702 * q^45 + 504 * q^46 - 660 * q^47 - 144 * q^48 - 585 * q^49 + 614 * q^50 - 153 * q^51 - 96 * q^52 + 528 * q^53 + 954 * q^54 - 1404 * q^55 + 400 * q^56 + 987 * q^57 + 252 * q^58 - 327 * q^59 - 936 * q^60 + 858 * q^61 - 1664 * q^62 - 1794 * q^63 + 384 * q^64 + 414 * q^65 + 288 * q^66 + 1587 * q^67 + 156 * q^68 + 1494 * q^69 + 216 * q^70 - 312 * q^71 - 24 * q^72 - 258 * q^73 + 856 * q^74 + 3231 * q^75 - 420 * q^76 + 708 * q^77 + 132 * q^78 - 1482 * q^79 - 576 * q^80 + 315 * q^81 - 2916 * q^82 - 138 * q^83 + 744 * q^84 + 108 * q^85 - 86 * q^86 - 3204 * q^87 - 72 * q^88 - 3084 * q^89 - 432 * q^90 + 2508 * q^91 - 1056 * q^92 - 2634 * q^93 + 612 * q^94 - 2016 * q^95 + 384 * q^96 + 1029 * q^97 + 2604 * q^98 + 1152 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.4.c.a	$18$	$4$	18.c	9.c	$3$	$2$	$1$	$1.062$	\(\Q(\sqrt{-3}) \)	None		✓			18.4.c.a	$2$	$0$	\(-2\)	\(0\)	\(9\)	\(31\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b	$18$	$4$	18.c	9.c	$3$	$4$	$2$	$1.062$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None		✓	✓		18.4.c.b	$2$	$0$	\(4\)	\(3\)	\(9\)	\(-19\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)